Homework 4 – Due
Thursday, Sep. 14, 11:59pm

Submitted on Blackboard
(learn.uncw.edu)

Three programs
based on material from Chapter 3.

Program 1: Count
Negative

Write
a Python program, CountNegative.py, which allows a user to enter as many
numbers as they want, one at a time.When they hit Enter with no input, the program will stop asking them for
numbers and prints out how many of the numbers were negative.The output also includes how many total
numbers were entered.Here is an example run:

Enter a number: 5

Enter a number: 6

Enter a number: -8

Enter a number: -4

Enter a number: 2

Enter a number: 0

Enter a number:

You entered 2 negative numbers out of 6 total numbers.

Program 2:
Calculating sin and cos

You can compute sin(x) and cos(x) using the following power
series:

Write a loop to calculate the sine
of a number input by the user.

·We can use math.pow(a,
b) to raise a number to a poweror
use a**b.

·To calculate the factorial of n, we can use math.factorial(n).

·Initialize a sum to 0.

·Each iteration of the loop adds a new term to a
running sum.

·In other words, in each loop iteration, for
sin(x), you would add sign*math.pow(x, count)/math.factorial(count) to a running sum.

·At the bottom of the loop, be sure to increment
the counter by 2 each time through the
loop.

·At the bottom of the loop, be sure to flip the
value of “sign”.Here’s a neat trick:Initialize sign
to 1.Then sign = -1*sign will make sign negative if it was
positive; it will be positive if it was negative.

·I would make a separate loop for calculating the
cosine to make thing simpler.

When does the loop stop?If we want our calculation accurate to 10
decimal places, we will set a flag to
stop the loop when the term being added
is less than 0.00000000001.

Here is an example run:

Input
a value in radians: 0.1

sin(0.1) = 0.0998334166

cos(0.1) = 0.9950041653

Here is another example run:

Input
a value in radians: 3.14159

sin(3.14159) = 0.0000026536

cos(3.14159) = -1.0000000000

Program 3: Is it
prime?

A prime number is an integer greater than 1 and divisible
only by itself and 1.The first seven
prime numbers are 2, 3, 5, 7, 11, 13, and 17.Write a program that asks the user for a positive integer and then tells
the user whether that number is prime or not.

How?Try dividing by
all the numbers smaller than the number (except 1).If the remainder is ever 0, then the number
is not prime.If you get through the
entire loop without ever finding a divisor that divides evenly into the number,
then it must be prime.